If $x \dagger y = x^{2}-3y^{2}$ and $x \otimes y = 3x^{2}-y^{2}$, find $4 \dagger (0 \otimes 1)$.
First, find $0 \otimes 1$ $ 0 \otimes 1 = 3(0^{2})-1^{2}$ $ \hphantom{0 \otimes 1} = -1$ Now, find $4 \dagger -1$ $ 4 \dagger -1 = 4^{2}-3(-1)^{2}$ $ \hphantom{4 \dagger -1} = 13$.